i thought that the last three didn't exsist because the square root was of a negative number when these were used, i know how to find limits but obviously i'm missing something here.
i was almost certain that sqrt(-) cannot be done for this,
please help me it's driving me mad

i thought that the last three didn't exsist because the square root was of a negative number when these were used, i know how to find limits but obviously i'm missing something here.
i was almost certain that sqrt(-) cannot be done for this,
please help me it's driving me mad

thanks in advance,
brittany

A limit exists for a function IFF

So right away it doesn't make sense for the limit to exist for 3, but not 4.

So let's look at it:

Now for we get:

we get:

we get:

is the one you had trouble with. Now you know that means it approaches 5 through negative values. But this doesn't always imply that we have a negative number. As x approaches 5 through negative values it must also pass through the interval , and these are non-negative. So we actually get:

And again, for and you are getting negative square root, so indeed, an illegal operation.